Von Neumann's theorem
In mathematics, von Neumann's theorem is a result in the operator theory of linear operators on Hilbert spaces.Let G and H be Hilbert spaces, and let T : dom ⊆ G → H be an unbounded operator from G into H. Suppose that T is a closed operator and that T is densely defined, i.e. dom is dense in G. Let T∗ : dom ⊆ H → G denote the adjoint of T. Then T∗T is also densely defined, and it is self-adjoint. That is,
and the operators on the right- and left-hand sides have the same dense domain in G.
